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Fraction - Alo Mathematics Centre

Fraction - Alo Mathematics Centre

What Are Fractions?

A fraction is a number that represents a whole number that has been divided into equal parts. For example, if you have a pie and you cut it into 4 equal slices, 1 of those slices is written as ¼.
A fraction can also represent a part of a group. For example, if you have 5 pieces of candy and you give 2 to your friend, those 2 candies are written as 2/5. If you have 5 pieces of candy and you give 2 to your friend, those 2 candies are written as 2/5.

A fraction is made up of two parts, the denominator and the numerator.
The denominator is the bottom number of the fraction. It is the number that represents the whole amount.
The numerator is the top number of the fraction. It is the number that represents the part of the whole.

Types of fraction

There are three (3) main types of fraction, which are;
1. Proper fraction
2. Improper fraction
3. Mixed fraction

Proper Fraction

This type of fraction is also known as balanced fraction. Simply because the numerator is smaller than the denominator, i.e. 2/3 , 5/7 , 4/9 , etc.

Improper Fraction

This kind of fraction has it numerator higher than the denominator, i.e. 4/3 , 7/5 , 3/2 , etc.

Mixed Fraction

It is also known as whole number fraction. It has a whole number and a proper fraction. For example, 1- 2/3, 4-7/8, 15-1/2, etc.
NOTE: I use dashes to separate the whole number from the proper fraction.

To be Continued.

Linear Equation

Linear Equation



Alo Mathematics CentreAn equation is a mathematical statement that shows equality between two expressions. There are different forms of equations; one of them is linear equation.
A linear equation is an equation on a straight line that contains one unknown.



Examples of linear equations are:
(a)  2x + 6 = 16
(b) 3x – 9 = 4x – 25
(c)  3(y + 2) = 8y + 10

Terms used in linear equation:
i.        Unknown: This is usually letters and it denotes missing number i.e x, y, etc.
ii.      Co-efficient: This a number placed together with unknown e.g. 2a, 3y.
iii.    Like terms: Terms are separated by addition or subtraction in an expression. So like terms are terms that can be combined.

Using different operations, linear equations are solved by finding values of different variables which are unknowns.

We must note that equations can be solved by;
1.     Adding the same number to both sides of the equation.
2.     Subtracting the same number to both sides of the equation.
3.     Multiply both sides of the equation by the same equation.
4.     Divide both sides of the equation by the same equation.


Examples:
1.      4a + 3 = 3a + 12. Find the value of a.

Solution

Collecting like terms:
4a – 3a = 12 – 3
A = 9

NOTE: When collecting like terms, this always happen (–) minus changes to plus and (+) plus changes to minus whenever both symbols crosses (=) equals to.

2.      Solve 3(b – 2) = 4(2b – 5)
Solution

Expanding and collecting like terms:
3b – 6 = 8b – 20 (Expanding in this type of question means multiplying the numbers in the bracket by the one outside the bracket)

3b – 8b = -20 + 6
-5b = -1
           
Dividing both sides by the co-efficient of b:

b = -14/-5
= 2 4/5 (2 whole number, 4 all-over 5)



3.     2y + 3 = 3y – 8

Solution

Collecting like terms:

2y – 3y = -8 – 3
-y = -11

Dividing both sides by the coefficient of y:

-y/-1   =   -11/-1
y = 11.

NB: Whenever unknown has no coefficient with it, and there is a negative sign known as minus before it, automatically the coefficient is 1.

Exercise your brain with the questions below:
1.     4(2m – 5) = 3(2m + 8)
2.     3x + 13 = 1
3.     6x – 2 = 2x + 8

ALO MATHEMATICS CENTRE implores every one of us to try and solve the questions above.

We will be expecting your response.

Thank You All.

Alomaths Cares
Multiple, Common Multiples and Least Common Multiple

Multiple, Common Multiples and Least Common Multiple



Lesson1:
Code: LE/02/2019
Topic: Multiple, Common Multiples and Least Common Multiple

Multiple


1.     Google Search Engine: a number that may be divided by another a certain number of times without a remainder. "15, 20, or any multiple of five"

2.     Pocket Oxford Dictionary: a number that contain another without remainder. (56 is a multiple of 7)

In this lesson you will learn what multiple of a number is. The idea of multiple came from multiplication table. 

Multiplication Table

Multiplication table is a list of multiples of a particular number, usually from 1 to 12.When you are learning your multiplication table you are learning multiples. For instance, when you divide a number by another number without any remainder that number is a multiple of the number you divided with i.e. the multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, etc, if you divide 28 by 7 the result is 4 remainder nothing. In that case, 28 is a multiple of 7.
If you are asked to list first ten (10) multiples of 2, 3, 4, 5 and 6. How do you go about it?

2 = 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20
3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30
4 = 4, 8, 12, 16, 20, 24, 28, 32, 36 and 40
5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50
6 = 6, 12, 18, 24, 30, 36, 42, 48, 54 and 60

The working above can only be achieved accurately by multiplying given numbers by integers. A multiple of a number is that number multiplied by an integer.

Integers

Integers are whole number, 2 is multiplied by 1 to get 2, by 2 to get 4, by 3 to 6 and so on. 1, 2, 3, etc, that 2 is multiplied by are called integers, they can either be negative or positive so other multiples of 2 are -2, -4, -6, -8, etc.

Common Multiples

These are numbers that appears with the multiples of two or more given numbers. The idea of common multiples should not be prolonged at all. Let take from the examples of multiples of numbers given above.

2 = 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20
3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30

If a cross checking is carried out well you will see that; within the multiples of 2 and 3 appears two or three numbers that are common i.e. 6, 12 and 18. Therefore, the common multiples of 2 and 3 are 6, 12 and 18.

Least Common Multiples

This simply means the lowest among the common multiples of two or more given numbers. In order not to prolong this part, we would take from the examples given above to solve lowest common multiples. The common multiples of two 2 and 3 are 6, 12 and 18 as solved above. Which of these multiples is the lowest multiple?  I am sure no one will choose 12 or 18. Therefore if 12 or 18 is not the L. C. M., 6 is the Least Common Multiple amidst the common multiples of 2 and 3.

The End.
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Introduction to Mathematics

Introduction to Mathematics



What is mathematics?


Mathematics according to

1.     Merriam Webster Dictionary:


·        the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations  èAlgebra, arithmetic, calculus, geometry, and trigonometry are branches of mathematics.
·        a branch of, operation in, or use of mathematics èthe mathematics of physical chemistry

2.     Pocket Oxford Dictionary:

·        The abstract science of number, quantity, and space, either as abstract concepts (pure mathematics), or as applied to other disciplines such as physics and engineering (applied mathematics)

3.     Live Science:

·        Mathematics is the science that deals with the logic of shape, quantity and arrangement.

4.     Alomaths:
·        Mathematics is the arithmetic of numbers.